Prolongements des difféomorphismes de la sphère. (Extensions of diffeomorphisms of the sphere) (Q1179590)

The main result of the paper is the following Theorem. There is no homomorphism \(\sigma\) of \(\hbox{Diff}^ \infty_ 0(S^ n)\) into \(\hbox{Diff}^ 1_ 0(B^{n+1})\) such that for every \(f\in\hbox{Diff}^ \infty_ 0(S^ n)\) the diffeomorphism \(\sigma(f)\) is the extension of f. Here \(\hbox{Diff}^ k_ 0(S^ n)\) and \(\hbox{Diff}^ k_ 0(B^{k+1})\) are the groups of diffeomorphisms of class \(C^ k\) of the sphere and the closed ball, respectively, that are \(C^ k\)-isotopic to the identity \((0\leq k\leq \infty)\).